Linear beam tubes have traditionally relied on axisymmetric solenoidal or PPM focusing to transversely confine the electron beam. In the particle accelerator community, however, it is well-known that alternating- gradient focusing using sequences of quadrupole magnets, known as "strong focusing", is capable of transporting more current for comparable field strengths. At mm-wavelengths, a key limitation to the peak and average power of vacuum electronics devices stems from the difficulty of control and confinement of high-current density beams. In this paper we summarize an ongoing design study of a strong focusing lattice employing permanent magnet quadrupoles (PMQs) capable of transporting a sub-mm radius electron beam for vacuum electronics applications. The study has the aim of producing a practical design for an experimental study at NRL for comparing quadrupole lattices with standard ones based on solenoidal periodic permanent magnets (PPMs). In addition, a design code and methodology for designing these PMQ channels is under development.